2009/11/30 by A. Losev, Andrei Losev, Sergey Slizovskiy · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.geomphys.2011.04.020
published as J.Geom.Phys.61:1868-1880,2011 · 16 pages, accepted to Journal of Geometry and Physics
arxiv created 2011/04/26 · openalex publication_date 2011/05/07 · arxiv updated 2011/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
Instantonic theories are quantum field theories where all correlators are determined by integrals over the finite-dimensional space (space of generalized instantons). We consider novel geometrical observables in instantonic topological quantum mechanics that are strikingly different from standard evaluation observables. These observables allow jumps of special type of the trajectory (at the point of insertion of such observables). They do not (anti)commute with evaluation observables and raise the dimension of the space of allowed configurations, while the evaluation observables lower this dimension. We study these observables in geometric and operator formalisms. Simple examples are explicitly computed; they depend on linking of the points. The new "arbitrary jump" observables may be used to construct correlation functions computing e.g. the linking numbers of cycles, as we illustrate on Hopf fibration.